Reachability算法

1.算法描述

Reachability在Wikipedia中的定义是这样的：
In graph theory, reachability refers to the ability to get from one vertex to another within a graph. We say that a vertex s can reach a vertex t (or that t is reachable from s) if there exists
a sequence of adjacent vertices (i.e. a path) which starts with s and ends with t.
Reachability是很有用的算法，比如说判断两地是否可达，社交网络中两人是否认识等。Reachability算法的思想很简单：从起始结点找其邻结点是否包含目的结点，如果不包含，继续找其邻结点的邻结点。以此类推，直到所有结点访问完。
但是，上述描述有一个小问题，如下图：



假设起始结点是A点，目的结点是B点。

第一步，A点不是目的结点B，找A的邻结点C，

第二步，C点不是目的结点B，找C的邻结点A、D，

第三步，A点不是目的结点B，找A的邻结点C，

……………………

现在问题就出来了，必须对结点的访问与否进行检查。

因此，Reachability算法步骤是：

起始点就是目的点，则可达且算法结束；
把当前结点标记为visited，找其邻结点，并判断邻结点是否包含目的结点；
重复第二步，直到找到目的结点，或者所有结点访问完。

值得一提的是，在Wikipedia中对Reachability还有这么一段描述：

In an undirected graph, it is sufficient to identify the connected components, as any pair of vertices in such a graph can reach each other if and only if they belong to the same connected component. The connected components of a graph can be identified
in linear time. The remainder of this article focuses on reachability in a directed graph setting.

所以，在Reachability算法还可以按照Connected Components算法思路，因此也就可以按照Connected Components中矩阵实现方法，用矩阵的幂的并集来实现Reachability算法。具体操作可以参照基于矩阵实现的Connected
Components算法。

2.算法实现

由于矩阵实现的方法和Connected Components算法类似，所以这里就只介绍非矩阵实现的代码：

def reachability(graph, srcVertex, dstVertex):
#     reachable = False
checkNode = []
checkNode.append(srcVertex)
while not(len(checkNode) == 0):
currentVertex = checkNode.pop()
if(currentVertex == dstVertex):
return True
else:
neighborIds = graph.get(currentVertex)
size = len(neighborIds)
for i in range(size):
checkNode.append(neighborIds[i])
return False

if __name__ == "__main__":
graph = {0: [1, 2], 1: [2, 3], 2: [3], 3: [4], 4: []}
print(reachability(graph, 4, 1))